One-Dimensional Electron Systems at Surfaces

Physics in one dimension :

• Elegant and simple

• Lowest dimension with translational motion

• Electrons cannot avoid each other

1D : • Collective excitations• Spin-charge separation

Giamarchi, Quantum physics in one dimension

2D,3D :• Electrons avoid each other

Localized e- (real space)Hubbard, t-J Models

• Different velocities for spin and charge

• Holon and spinon bands intersect at EF

Two Views of Spin Charge Separation

Holon

Hole

Spinon

EF

k

E

Spinon

Holon

Delocalized e- (k-space)Tomonaga-Luttinger Model

Atomic Chains as the Ultimate Nanowires

• Straight steps at vicinal Si(111)7x7( 1 kink in 20 000 edge atoms )

• Metallic surface states in the gap of silicon (truly 2D)

Clean

"Decoration" of Steps⇒ 1D Atomic Chains

With Gold1/5 monolayer

Si chain

Si dopant

x-Derivative of the Topography, “ Illumination from the Left ”

Many metals create chains

Li, Na,…Ca,Ba,…In Ag, AuPt Gd,Ho,Dy,Ce

Also on Si(100), GaAs(110)

Au

Graphitichoneycomb chain

drives the surface one-dimensional

Variable chain

spacing, coupling

2D

Fermi Surfaces from 2D to 1D

2D + super-lattice

1D

t1/t2 ≈ 40 10

kx

1D/2D Coupling Ratio

Tight Binding Model

Fermi Surface Data

t1/t2 is variable from 10:1 to > 70:1 via the step spacing

t2

t1

8/3 e- per chain atom (spins paired)5/3 e- per chain atom (spin split)

Crain et al., PRL 90, 176805 (2003)

Fractional Filling

Augraphitic

Fractional Fillingvia Indirect Doping

1D analog of HiTc doping

Si(553) - Au

3x1 cell

2 Si3 Au

Fractional Chargeat the End of a CDW / Chain Segment

Seen for 2x1 (polyacetylene) : Su, Schrieffer, HeegerPR B 22, 2099 (1980)

Predicted for 3x1 : Su, SchriefferPRL 46, 738 (1981)

Suggested for Si(553)3x1-Au : Snijders et al.PRL 96, 076801 (2006)

Is there Spin-Charge Separation ?

Bands remain split at EF

⇒ Not Spinon + Holon

Losio et al., PRL 86, 4632 (2001)

Why two half-filled bands ?~ two half-filled orbitals

~ two broken bonds

EF

Proposed by

Segovia et al., Nature 402, 504 (1999)

Si(557) - Au

hν= 34 eV

E [eV]

Sanchez-Portal et al. PRL 93, 146803 (2004)

LDA Calculation Predicts Spin Splitting

Non-magnetic constituents !

Adatoms

Step Edge

Si-Au Antibonding

Si-Au Bonding

E (eV)

0 ZB1x1

Adatoms

ZB2x1

kx

EFSpin-split band, similar to that in photoemission

Si(557) - Au

Si AdatomsAu

GraphiticHoneycomb

Chain

First Principles Calculations:Crain, Erwin, et al.,PRB 69, 125401 (2004) Sanchez-Portal et al.,PRB 65, 081401 (2002)

X-Ray Diffraction:Robinson et al., PRL 88, 096104 (2002)

Spin-Split Band

Si(557) - Au

Evidence for Spin–Splitting

E [eV]

kx [Å−1]

• Avoided crossings located left / right for spin-orbit (Rashba) splitting.

• Would be top / bottom for non-magnetic, (anti-)ferromagnetic splittings.

Barke et al., PRL 97, 226405 (2006)

Si(553) - Au

Nanoscale Phase Separation in 1D

1 Erwin, PRL 91, 206101 (2003) 2 McChesney et al., Phys. Rev. B 70, 195430 (2004)

Si(111)5x2 - Au

• Doped and undoped segments ( 1D version of “stripes” )gap ! metallic

• Competition between optimum doping1 (5x8)and Fermi surface nesting2 (5x4)

• Compromise: 50/50 filled/empty (5x4) sections

What Determines theLength of the Segments ?

Barke et al., unpublished

Spectroscopy +0.8V

-1.2V Topography +0.8V

Use semiconductor substrates

• Metal atoms locked to the substrate

• Electrons at EF decouple (in the gap)

• Tunable band filling, fractional 5/3

• Tunable chain coupling, 10:1 to >70:1

• Tunable magnetic moment (rare earths)

⇒ New playground for low-dimensional physics

Overview: Crain and Himpsel, Appl. Phys. A 82, 431 (2006)